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We provide an alternative proof of the classical single-term asymptotics for Toeplitz determinants whose symbols possess Fisher-Hartwig singularities.
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P. Deift, A. Its, I. Krasovsky, X. Zhou. The Widom-Dyson constant and related questions of the asymptotic analysis of Toeplitz determinants. Proceedings of the AMS meeting, Atlanta 2005. J. Comput. Appl. Math. 202
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I. V. Krasovsky. Correlations of the characteristic polynomials in the Gaussian Unitary Ensemble or a singular Hankel determinant. Duke Math. J. 139
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P. Deift, A. Its, I. Krasovsky. Asymptotics of the Airy-kernel determinant. Commun. Math. Phys. 278
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J. Baik, P. Deift, K. Johansson, On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc. 12
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P. Deift, T. Kriecherbauer, K. T-R McLaughlin, S. Venakides, X. Zhou. Strong asymptotics for orthogonal polynomials with respect to exponential weights. Commun. Pure Appl. Math. 52
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P. Deift, Integrable operators. Differential operators and spectral theory, 69–84, Amer. Math. Soc. Transl. Ser. 2, 189, Amer. Math. Soc., Providence, RI, 1999
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T. Ehrhardt. A status report on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities. Operator Theory: Adv. Appl. 124
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E. W. Barnes. The theory of the G G -function. Quart. J. Pure and Appl. Math. 31
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M. Bertola. The dependence on the monodromy data of the isomonodromic tau function. arXiv:0902.4716
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P. Deift, A. Its, I. Krasovsky. Toeplitz matrices and Toeplitz determinants under the impetus of the Ising model. Some history and some recent results. In preparation
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M. Bertola. Moments determinants as isomonodromic tau functions. Nonlinearity, 22
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